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Related Concept Videos

Student t Distribution01:31

Student t Distribution

The population standard deviation is rarely known in many day-to-day examples of statistics. When the sample sizes are large, it is easy to estimate the population standard deviation using a confidence interval, which provides results close enough to the original value. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
The Student t distribution was developed by William S. Goset (1876–1937) of the...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
Comparing Experimental Results: Student's t-Test01:09

Comparing Experimental Results: Student's t-Test

The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...

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A Tablet-Based Curriculum-Based Measurement Protocol for Kindergarten Writing
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A Tablet-Based Curriculum-Based Measurement Protocol for Kindergarten Writing

Published on: February 7, 2025

Bounded asymmetrical Student's-t mixture model.

Thanh Minh Nguyen, Q M Jonathan Wu

    IEEE Transactions on Cybernetics
    |July 30, 2013
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new bounded asymmetrical Student's-t mixture model (BASMM) for pattern recognition. This robust model effectively handles non-Gaussian, asymmetric, and bounded data, outperforming traditional Gaussian mixture models.

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    Published on: July 3, 2020

    Area of Science:

    • Computer Vision
    • Pattern Recognition
    • Statistical Modeling

    Background:

    • Student's-t mixture models offer robustness but are unbounded and symmetric.
    • Real-world data often exhibit asymmetry and bounded support.
    • Existing models struggle with these data characteristics.

    Purpose of the Study:

    • To introduce a novel finite bounded asymmetrical Student's-t mixture model (BASMM).
    • To develop a flexible distribution capable of modeling diverse data shapes, including asymmetric and bounded data.
    • To present an alternative parameter estimation method for Student's-t mixture models.

    Main Methods:

    • Proposed an extension of the Student's-t distribution to accommodate bounded and asymmetric data.
    • Developed a new parameter estimation approach that directly optimizes the Student's-t distribution.
    • Introduced a model that includes Gaussian mixture models (GMM) and Student's-t mixture models (SMM) as special cases.

    Main Results:

    • The BASMM demonstrated flexibility in fitting various data distributions, including non-Gaussian, asymmetric, and bounded data.
    • Each component of the BASMM can model data within different bounded support regions.
    • The proposed estimation method avoids representing Student's-t distributions as infinite Gaussian mixtures.

    Conclusions:

    • The BASMM is a powerful and flexible tool for pattern recognition tasks with complex data.
    • The model shows promise for applications like image segmentation, handling bounded and asymmetric data effectively.
    • The new estimation method offers a direct and efficient way to fit the proposed model.